(C) Given the equation $2 \cosh^2 x - 3 \sinh x - k = 0$. Using the identity $\cosh^2 x = 1 + \sinh^2 x$,we substitute this into the equation: $2(1 +

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(C) Given the equation $2 \cosh^2 x - 3 \sinh x - k = 0$. Using the identity $\cosh^2 x = 1 + \sinh^2 x$,we substitute this into the equation: $2(1 + \sinh^2 x) - 3 \sinh x - k = 0$ $2 \sinh^2 x - 3 \sinh x + (2 - k) = 0$. Let $t = \sinh x$,where $t \in R$. The quadratic equation $2t^2 - 3t + (2 - k) = 0$ has no real solution for $x$ if the discriminant $D $D = (-3)^2 - 4(2)(2 - k) $9 - 8(2 - k) $9 - 16 + 8k $8k - 7 $k < \frac{7}{8}$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $k \in R$ is such that the equation $2 \cosh^2 x = 3 \sinh x + k$ has no real solution,then which of the following is correct?

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A
$k < \frac{1}{2}$
B
$k < \frac{3}{8}$
C
$k < \frac{7}{8}$
D
$k < \frac{5}{8}$

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4-2.Quadratic Equations and Inequations

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If $k \in R$ is such that the equation $2 \cosh^2 x = 3 \sinh x + k$ has no real solution,then which of the following is correct?

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